A Comparative Survey of Modeling Absorption Tower Using ...

Journal of Chemical and Petroleum Engineering, University of Tehran, Vol. 45, No.1, June 2011, PP. 57-70 57

* Corresponding author: Tel: +98- 21- 66957784 Fax: +98- 21- 66957780 Email: [email protected]

A Comparative Survey of Modeling Absorption Tower Using Mixed Amines

Mohammad Samipoor Giri1, Mahdi Akbari2, Mojtaba Shariaty- Niasar*2 and Afshin

Bakhtiari2 1 Chemical Engineering Department, Islamic Azad University, North Branch ,

Tehran, Iran 2 School of Chemical Engineering, College of Engineering, University of Tehran,

Tehran, Iran (Received 2 July 2011, Accepted 20 June 2011)

Abstract In natural gas treatment, the removal of CO2 and H2S in acid gases is a critical concern. There are various purification technologies that can be used for the removal of acid gas impurities. Absorption of acid gas into amines is one preferred method in gas industries. In the past, single amines was used, but recently in order to improve absorption performance, mixed amines with different solubility and reaction rates have been used. In this study, artificial neural network ANN is used as a method to model the absorption tower when uses mixed amines. A specified model which is simple in calculation and good in accuracy was developed. In this model back propagation learning is used and the corresponding parameters have been optimized. Finally, the new method has been compared with conventional mass transfer and equilibrium methods. The obtained results confirmed the simplicity and accuracy of the developed method.

Keywords: Absorption tower, Mixed amines, Artificial neural network, Mass transfer method, Equilibrium method

Introduction The gas purification for removing impurities, such as CO2 and H2S, is one of the main parts of natural gas (NG) treatment industry. For this process, the most important alkanolaminesused, are monoethanolamine (MEA), diethanolamine (DEA), di-isopropanolamine (DIPA) and N-methyldiethanolamine (MDEA) [1]. Since mid-80s of 20th century, mixed alkanolamines have been used. That was simply due to enhance absorption performance of alkanoamines. Mixed amines can provide any degree of selectivity and absorption rate [2].So modeling and simulation of amine absorption tower with amine mixtures as absorption solvent are very useful. It is many years now that the simulation and modeling of amine absorption tower in natural gas sweetening process has been studied [3]. With respect to the accuracy and fast calculations; two main methods namely; "equilibrium" and "mass transfer"; were developed. Basing on fundamental

principles, either individual method has its own subdivisions. Comparing to mass transfer method, low accuracy is the main disadvantage of the equilibrium method which is capable of faster calculation. On the other hand, hydraulic parameters of absorption tower and other details that are used in mass transfer method make the calculation more complicated and time consuming [3-4]. In order to overcome such disadvantages, another method should be developed. So, for modeling absorption tower, ANN methods applied, because of its ability to solve nonlinear complicated equations with higher speed and better accuracy.

Methods of modeling the amine absorption tower Absorption of H2S and CO2 in a solvent is consisted of two successive mechanisms of mass transfer and reaction. When the acid gases are diffused into the liquid, they react with solvent and leads to unstable products after which the solvent is recovered [5]. In

58 Journal of Chemical and Petroleum Engineering, University of Tehran, Vol. 45, No.1, June 2011

order to determine the capacity and rate of absorption, modeling of amine absorption process is carried out by using some known parameters such as; the percent of acid gases in feed, the amount of circulating solvent, operating temperature and pressure, amine concentration and amine loading [6].

Equilibrium method In this method, vapor and liquid are entered a column, pass over the tray or flow through packed bed, exchange the materials and energy and then left in equilibrium [5].At this stage, the concentration of inlet gas and output liquidis calculated, using experimental data (as equilibrium curves) or using thermodynamic relation (such as equation of state).

Followings are equilibrium equations for H2S and CO2absorption in amine solvent that were presented by Dankwerts and Mc Neil for the first time [4]. Other researchers accounted for the constants of equilibrium equations, using empirical studies [7].

Generally for H2S/CO2/amine/H2O system, with two known parameters (αH2S, αCO2), the 13 following unknowns parameters could be calculatedby equation 10 to 20 [8].

The equations 17 to 20 are determined from mass and electric charge balance. K1 to K7are temperature dependent variables and can be calculated using empirical data. Considering equations 10 to 20, the following 3 equations can be written for calculating pressure of H2S and CO2 and also concentration of [H+].

1' '2

KRR NH H RR NH (1) 2' '

3KR RNCOO R RNH HCO (2)

32 2 3

KH O CO H HCO (3) 4

2KH O H OH (4)

5 23 3

KHCO H CO (5) 6

2KH S H HS

(6) 7 2KHS H S (7)

2 2 2*C O C OP H C O (8)

2 2 2*H S H SP H H S (9)

2 ' ' '

2 CO H S 2 32 2

2

2 3

[H S], [S ], P , P , [RR N H ], [ ], [RR ], [ ], [ ],

[ ], [ ] , [ ], [ ]

H NH RR N CO O H CO

C O O H CO H S

'

1 '2

H R R N HK

R R N H

(10)

'3

2 '

RR NH HCOK

RR NCOO

(11)

3

32

H HCOK

C O

(12)

4K H OH (13) 23

53

H COK

HCO

(14)

A Comparative Survey of ….. 59

62

H H SK

H S

(15)

2

7

H SK

HS

(16)

' ' '2m RR NH RR NH R RNCOO (17)

2

22H Sm H S H S S (18)

2

' 23 2 3C Om R R N C O O H C O C O C O (19)

' ' 2 22 3 32 2RR NH H RR NCOO HCO OH CO HS S (20)

2 2

2

2

2

2

6 7

7

1

H S H SH S

H SH S

H Pm H

K K HP

HK

(21)

2 2

2

2

2

2

3 5

"

2 5

1

CO CO

CO

CO

CO

H Pm H

K K HP

H m H

KS K K K

(22)

2 2

2 2

2 2

"

2 51 4 1

"

1 1

2 5 2 "

1 1CO H S

CO H S

CO H S

P PK KK K K KH m m

m Hm K K H H H K HK K K H

K

(23)

Where in equation 22 and 23, K” is equal

to:

2

2

3"

1 2

1 CO

CO

H P KK

K K H H

It is important to note that with these equations, one can calculate the theoretical numbers of required trays, which can then be multiplied by tray efficiency to obtain the real numbers. The reported amount of efficiencies in such systems is 0.1 to 0.4 [3].Maddox et al worked on some gas purification units, using this method. Their results are shown in table 1[9-10].

It is obvious that the theoretical number of trays that were calculated with this method is quite different than those of real. This large discrepancy is due to the fact that

the hydraulic parameters of absorption tower are not accounted for.

Table 1: Results of Maddox et al

Unit number 1 2 3 4

Real number of trays 25 20 15 30

Theoretical number of trays 2 4 2 2

Mass transfer method In this method each tray is considered as a mass transfer stage between liquid and gas. The output stream conditions are calculated, using tray mass balance, while assuming the plug flow for gas phase and complete mixing of liquid on each tray. Variation of acid gas mole fraction in gas phase on tray K, are calculated by the following equations [10]:


'

00

10

'0

1

11,...,

A

A

jj v Ayn

i yj

i j Ay

n

i v Ayi

dyF N AN dz

yN For j n

dF N AdZ

(24)

While for the components that is not absorbed; Fyi=Constant for j=nA+1,…,nG The boundary conditions are as follows:

,

,

0,

1,...,,

ini i k

inK

G

f j j k

K

For Z y y

F Fand For j n

For Z h y yF F

(25)

,in in

k j kF and y are the flow rate and the mole fraction of gas stream input to the tray respectively. They are obtained from output stream data of the next tray K+1.To calculate flow rate and composition of the liquid phase, the kinetics of reaction of acid gas-

amine should be known. Generally this reaction could be as:

1,1 ,1 ,111 1

pR

j j

nnG L L

A R j P jj j

A R P

(26)

2,2 ,2 ,221 1

pR

j j

nnG L L

A R j P jj j

A R P

(27)

Liquid flow rate and the corresponding component concentrations are calculated according to reaction rate of acid gas and amine. Since acid gas reaction with different amines has different reaction rate, determination of xj,K is depended on Hatta number (Ha) which is defined as:

11

1.

1 21

RRj

A

n mmA A j Ab

jL A A

Ha a KC CR DK m

For 3<Ha; xj,K=0 for j=1,………..…,nv For 0.3<Ha <3 (28)

,

' ' ', , 1 1 , 1

1,...,j k L

j k k wk j k k w vk j v F j j j v L F Ly y

v v m

x L w x L x w N A h a r A y h

For j n n n

(29)

,

' ', , 1 1 , , , 1

1,...,j k

in inj k k wk j k k w vk j k K j k k j j j v L F L

v m v m s

x L w x L x w y F y F a r A y h

For j n n n n n

(30) There are similar relations for other components which are not absorbed. Absorption flux of different species is also obtained from the equation 31:

', ,0

1,...,j G j t i j j k Aky iN K P y H x For j n

(31)

And with application of Fick’s law it could be written as:

00

1,...,jj j K Ay

y

dxN D C For j n

dy

(32)

1,...,L

L

jj j K i Ay y

y y

dxN D C For j n n

dy

(33)

To determine the amount of flux, the concentration profile of absorption species is obtained from the following second order differential equation:

2,

2 1,...,j j jj j v M

y k

d x aD r For j n n

d c (34)


For solving equation 34, boundary conditions should be determined. Tray temperature is calculated by enthalpy balance around each tray as equations 35 to 38:

,

' '

1 1 , 1 , , , , , 1 1 1 , 1 ,1 1 1 1

1 1 , 1 , , , ,1 1 1 1

G GL L

G GL A

j K

n nn n

K K j K L j K K j k G j wk K j k L j K K wk j K G jj j j j

n nn nC abs R

vK VK Vj K G j wk VK w L j K j K j Kj j j j

T L x Cp T F y Cp w L x Cp T F V y Cp

T V y Cp T w x Cp Q Q Q

(35) (36)

, , , 1, .. .,a b s a b s in inj K j K j k K j k AQ H F y F y F o r j n (37)

,

' '

, , , , 1 , 1

,

11, ...,

j k

R R in in

j K j K j k K j k j k k wk K j K vk w E

j j

Q H F y F y x L w L x w x For j na

(38)

The above equations planned for all trays in the tower and are solved simultaneously. A computer program is written to solve such equations [11-18].

Artificial neural network An artificial neural network (ANN) is a mathematical model that is inspired by the biological neural networks and it is mostly an adaptive network whose structure can be modified basing on the information that flows through the network during the learning period [19]. In the learning process, neural networks are subjected to a set of training data together with corresponding outputs. After a sufficient number of training, the neural network learns the patterns of input data and creates an internal model which is then used to make predictions for new inputs. The foundation of ANN is the neuron or processing element (PE) (Fig .1). Each processing element, receives an input vector I, (Ii1, Ii2, Ii3…Iin].The processing element calculates an output Oi, by using a sigmoid function.

11 exp( )i i

i

O f II

The PEs are arranged in a special

topology or architecture. Several possible architectures have been used, however the most common one is the multi – layer back – propagation architecture.

Figure 1: A typical neuron in the hidden layer

The back propagation algorithm is used in layered feed-forward ANN. This algorithm is applicable to a wide range of problems and is the predominant supervised training algorithm. The term back propagation indicates the method by which the network is trained, and the term supervised learning, implies that the network is trained through a set of available input – output patterns. In this algorithm the neurons are organized in some layers, and send their signals forward, and then the errors are propagated backwards. Initially, all the weights are set randomly and input data are multiplied by weights and entered to the input layer of network, and the output of the network is given by a function which determines the activation of the neuron. Supervised learning is used in the back propagation algorithm to provide the algorithm with examples of the desired inputs and outputs, and then the error is calculated. The network is repeatedly exposed to these input – output relationships and the weights among the neurons are continuously adjusted until the network learns the correct input – output behavior.


The back propagation algorithm is desired to reduce the error that is propagated back through the network and is used to update the weights among neurons iteratively. This update process is repeated for all patterns many times until the network becomes capable of reproducing the input – output relationships to within an acceptable small tolerance. There may be some intermediate hidden layers (Fig 2) [16-19].

Figure 2: A one hidden layer feed and neural network

The output neuron from the hidden layers and the output layers are also given by the following equation. In this case the input Ii to a neuron in these layers is calculated by:

i ij j iB Bj

I W O W O

Where the sum over j represents all neurons in the previous layer and OB is an invariant output from the bias neuron. The weight Wij represents the connection weight between neurons I and j and the weight WiB is the connection weight between neuron i and the bias neuron.

Data Analysis Effective parameters for the design of amine absorption tower are classified into several categories. The first ones are the parameters related to the absorbent solvent such as; the type, concentration, allowable loading amount and the solvent smell. The second category consists of parameters related to input sour gas such as; flow rate, temperature, pressure and the third category

is about parameters related to how to use sweet gas which is, the percentage of allowable concentration of acid gas in output sweet gas and so on. In designing an amine absorption tower, with application of amines mixture, the optimized percent of amine mixture in water is also a significant parameter. In this study all the above parameters for amine mixture absorption tower were extracted fromvarious gas refineries all over the world, which covers nearly 1200 data. These data contain designing conditions, operating conditions and test runs of sweetening units[20-22]. In network training, back propagation was used and the applied network was a 2-4-6-4 with figure 3in which sigmoid function has been chosen as neuron logistic function.

Figure 3: Structure of applied artificial neural

network in this study

Network parameters such as number of layers, number of neurons in each layer, learning rate, error factor and etc, are utilized in various conditions and are simulated to reach the maximum rate of convergence and accuracy of calculation.

Result and discussion Fajr jam refinery was chosen as a case

study and three methods (equilibrium, mass transfer and artificial neural network) were used for simulation of absorption tower. Table 2presents the characteristics parameters together with operating conditions of amine absorption tower in the Fajr Jam refinery.


The test run data of Fajr Jam refinery (1999) for amine mixture in absorption tower

are shown in table 3. These were used as reference data in current simulation [20].

Table 2: Characteristics parameters and operating conditions of amine absorption tower in the Fajr Jam refinery

Parameter Value Diameter (m) 3.7

Number of Trays 32 Tray Valve

Tray Spacing (m) 0.61 Passes 1,2

Diameter of Valve (m) 0.048

Weir Height (m) 0.076 Down Comer Clearance (m) 0.038

Down Comer Width (m) 0.297

Feed Tray 1, 32

Table 3: Data of Fajr Jam refinery for amine mixture absorption

Sour gas flow rate (MMSCMD)

Amine C. R. (Cu m/hr)

Reboiler Steam

(ton/hr)

MDEA (%wt)

DEA (%wt)

H2S (mg/scm)

CO2 (ppm)

5 252 25 22.42 11.6 1.84 - 10 252 25 22.42 11.6 1.8 354 14 252 25 24.8 12.3 1.8 1300 14 252 32 23.4 11.8 1.8 1450 14 270 32 26.62 12.18 1.6 763 14 300 34.5 26.61 13.4 1.84 426 14 300 38.4 25.7 14.3 1.6 403 14 300 38.4 25.1 17 0.92 136 14 300 38.4 26 18.24 1.8 25.5 14 300 38.4 26.2 18 0.87 47.4 14 300 38.4 26.3 18.2 0.9 40 14 300 38.4 24.82 17.65 1.5 49 14 300 38.4 25.99 17.75 1.8 14.5 14 300 38.4 26.52 18.27 1.57 - 14 300 38.4 24.77 17.77 0.9 24.6 14 300 38.4 24.41 20.1 1.2 22.58 14 300 38.4 25.2 20.32 1.1 26 14 300 38.4 23.32 19.51 1 15.32 14 280 35.32 25.37 19.84 1 14.7 14 252 34 22.47 19.41 1 23.1


Modeling and simulation results Equilibrium method: Simulation and modeling result of Fajr jam refinery and five other gas sweetening refineries (case 1 to 6) which was done by equilibrium method, are shown in table 4. The calculation basis of amine circulation rate in each case was concentration of CO2 and H2S in output stream. As shown in the table, the simulation results have an average accuracy. However the main problem the method is its inability of computing temperature, pressure and concentration profile of the components along the tower [7]. In fact, this method can just calculate the acid gas percentage in output sweet gas using of known input data. Because of trial and error procedure used in this method, the calculation speed was low.

Mass transfer method: By applying film theory and mass transfer method procedure, absorption tower of Fajr jam refinery and five other gas sweetening refineries (case 1 to 6) has been simulated. Results are shown in table 5. As shown in the table, the results have very good accuracy that is due to the fact that in the simulation, the hydraulic condition of the absorption tower is also taken into account. The speed of this method is lower than equilibrium method, because of complicated equations. The determining basic parameter of amine circulation rate in each case was the concentration of CO2 and H2S in output stream.

Table 4: Simulation results for various refineries by equilibrium method

Case %H2S %CO2 %MDEA %DEA %MEA Amine C. R Actual Sim

1 2.5 1.2 35 15 - 290 278 1 2.1 1.1 35 15 - 240 230 1 2.6 1.6 34 16 - 310 301 2 0.8 4.1 24.4 17.65 - 65 83 3 16.1 1 32 18 - 43 51 4 4.5 2.3 45 5 - 155 140 5 0.81 3.1 40 10 - 120 115 5 0.77 2.5 38 12 - 143 150 6 3.2 1.8 35 - 15 21 30

Table 5: Simulation results for various refineries by mass transfer method


1 2.5 1.2 35 15 - 290 292

1 2.1 1.1 35 15 - 240 235

1 2.6 1.6 34 16 - 310 318

2 0.8 4.1 24.4 17.65 - 65 66

3 16.1 1 32 18 - 43 40

4 4.5 2.3 45 5 - 155 149

5 0.81 3.1 40 10 - 120 118

5 0.77 2.5 38 12 - 143 150

6 3.2 1.8 35 - 15 21 25


Temperature, pressure and H2S

concentration profiles along the absorption tower are shown in figures 4 - 6. As shown in fig 4, the tower temperature rises sharply and then decrease gradually till reach to a stable condition at the top of the tower. This is due to a large absorption heat of reaction that is released in lower trays and its gradual decrease long the tower. Artificial neural network method: By building a 2-4-6-9 network, followed by its training using more than 700 input

data, the weights between neurons are clarified. This network has been surveyed by all existing parameters such as the number of neurons in each layer, the amount of hidden layers and the error factor in the network. Then it is optimized to the minimum error. This network has also been used for simulation of absorption tower of Fajr jam refinery and five other refineries (case 1 to 6) and the obtained result have been demonstrated in table 6.

Figure 4:Temperature profile along the absorption tower

Figure 5:Pressure profile along the absorption tower

Figure 6: H2S Concentration profile along the absorption tower


As shown in table 6, data conformity with the actual data is much better than those in the equilibrium method and has as good accuracy as in mass transfer method. Also

ANN can present all profiles of temperature, pressure and H2S concentrations (figures 7, 8, 9).

Table 6: Simulation results for various refineries by artificial neural network method


1 2.5 1.2 35 15 - 290 288 1 2.1 1.1 35 15 - 240 242 1 2.6 1.6 34 16 - 310 315 2 0.8 4.1 24.4 17.65 - 65 75 3 16.1 1 32 18 - 43 45 4 4.5 2.3 45 5 - 155 152 5 0.81 3.1 40 10 - 120 123 5 0.77 2.5 38 12 - 143 150 6 3.2 1.8 35 - 15 21 19

Figure 7: Temperature profile along the absorption tower

Figure 8: Pressure profile along the absorption tower



Figure 10a: Temperature profile along the absorption tower

Figure 11: Pressure profile along the absorption tower



Convergence rate of calculation in this method is approximately in the order of millisecond and by doing some simple modification, simulation results are obtainable for other absorption tower. Figures10a-calso; show the comparison of mass transfer method with neural network methods for calculating absorption tower profiles. As shown in these figures, the results obtained by artificial neural network are as good as mass transfer method.

Conclusion Considering this comparative survey, it has been clarified that neural network method is a good new method in simulating absorption towers of amine units. Its accuracy is better than that in equilibrium method while it is comparable to mass transfer method. Neural network method is also able to compute temperature, pressure and concentration profiles of components. This specification is in contrast to the equilibrium method. On the other hand, the simplicity of calculation and convergence rate of neural networks method is much better when compared with those in equilibrium and mass transfer methods. Finally, sigmoid logistic function is capable for information processing of absorption tower. Nomenclature Aj Absorbed component j A Stoichiometric coefficient Av Gas – liquid interfacial area per unit

volume of liquid (m2/m3) Av

’ Gas – liquid interfacial area per m3 froth on the plate (m2/m3)

av' Interfacial area per unit volume of packed column (m2/m3)

CA Molar concentration of component A (kmol/m3)

Ck Total molar concentration in the liquid on plate k (kmol/m3)

cp Specific heat (kJ/kmole K) D Molecular diffusivity (m2/h) dk Column diameter (m) F Total molar gas flow (kmol/h) FA Enhancement factor

Fk Molar gas flow rate leaving plate k (kmol/h)

Hj Henry’s coefficient for absorbed component j (bm3/kmol)

Ha, Hatta Number Ha” Modified Hatta number -∆ Hj

abs Heat of absorption of component j (kJ/kmol)

-∆ HjR Heat of reaction of component j

(kJ/kmol) hF Froth height on plate (m) Kj Equilibrium constant of component j kj Reaction – rate coefficient of component j kG, Aj Gas – solid mass –transfer coefficient

for absorbed component Aj (m/h) L Volumetric liquid flow rate (m3/h) L’ Molar liquid flow rate (kmol/h) L0

’ Molar flow rate of liquid feed to column (kmol/h)

Lk’ Molar flow rate of liquid stream leaving

plate k (kmol/h) mj,IReaction order with respect to component

j in reaction i M Molecular weight (kg/kmol) m Reaction order

0j yN

Interfacial flux of component j per

unit gas – liquid interfacial area (kmol/m2h)

nA Number of absorbing components nE Number of reactions in the liquid phase nG Total number of components in gas phase nL Total Number of components in liquid

phase nM Number of gas – phase components

involved in moderately fast reactions nP Number of reaction products in the liquid

phase nR Number of reactants in liquid phase. nS Number of gas – phase components

involved in very slow reactions nV Number of gas – phase components

involved in very fast reactions p Partial pressure (b) pt Total pressure (b) Pj Product j r Reaction rate (kmol/m3h) Rj Liquid – phase reactant j Qj,k

abs Total heat of absorption of component j on plate k (kJ/h)


QkC Total heat of cooling taken away from

plate k (kJ/h) Qj,k

R Total heat of reaction of reaction j on plate k (kJ/h)

Tk Temperature of intermediate gas feed to plate k (K)

Tvk Temperature of intermediate gas feed to plate k (K)

Twk Temperature of intermediate liquid feed to plate k (K)

Vvk Flow rate of intermediate gas feed to plate k (kmol/h)

Vwk Flow rate of intermediate gas withdrawal from plate k (kmol/h)

xj Mole fraction of component j in the liquid bulk

xj,k Mole fraction of component j in the bulk of the liquid stream leaving plate k

,j kwx Mole fraction of component j in the intermediate liquid feed to plate k

y Coordinate perpendicular to the gas – liquid interface (m)

jFy Location of reaction front of reaction j (m)

yG Gas – film thickness (m) yj Mole fraction of component j in the bulk

of the gas phase yj,k Mole fraction of component j in the bulk

of the gas stream leaving plate k yL Liquid – film thickness (m)

,j kvy Molar fraction of component j in the intermediate gas feed to plate k

z Axial coordinate in the froth on the plate (m)

Greek symbols L Liquid hold – up of packing or fraction

of liquid in the froth L Liquid density (Kg/m3)

A Active area of plate (m2)

Loading of acid gas

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